In manufacturing devices that include precision discrete devices (e.g., manufacturing microelectronic chips on silicon substrates), there is an ever growing need to improve manufacturing processes. Improving manufacturing processes may require, among other things, monitoring the characteristics of manufactured devices and adjusting input parameters (e.g., equipment controlling parameters) that influence the characteristics of the manufactured devices. A mechanism used for automatically monitoring information relating to the processing of manufactured devices and estimating the characteristics of these manufactured devices based on the adjustments to input parameters is called a process model. In turn, an automated system that makes adjustments to the input parameters as estimated by the process model and uses the adjusted input parameters to control the manufacturing processes is called a control system (or a process control system).
A conventional process model for one or more pieces of manufacturing equipment to be used in manufacturing processes is referred as a predictive model, which attempts to predict the characteristics of manufactured devices based on the input parameters. One example implementation of a conventional predictive model may use a lookup table, without using a mathematical model, to determine the best combination of input parameters to control the characteristics of manufactured devices. This technique however often requires collecting and storing an enormous corpus of experimental data obtained from numerous real-time trials. These drawbacks make this example technique a complicated, time-consuming and costly procedure.
Another conventional process model is a mathematical or formula based optimization method. This model uses numerical analyses to solve equations. More specifically, using a mathematical formula, an equation or a set of equations is used to calculate output values and arrive at the minimum of an objective function. The minimum represents an optimal solution of the objective function. More often than not, the formula is of a complex structure which may be difficult to solve. The above-described formula technique, which uses equations built on the basis of a limited number of empirical data points, can be rapid and compact. However, it is not configured to store and take into account the “history” of collected empirical data points. For example if empirical data points are collected within a small part of the total area over which monitoring and potential adjustment may be desired, the resulting correction provides a case of close fit only for the small part of the total area from which the empirical data points were collected, but when this correction is extrapolated over the total area as is widely practiced today, the resulting predictions can become inaccurate.